Globalization of twisted partial actions

Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.Comment: 27 pages. To appear in Trans. Amer. Math. Soc

There is no analog of the transpose map for infinite matrices

In this note we show that there are no ring anti-isomorphism between row finite matrix rings. As a consequence we show that row finite and column finite matrix rings cannot be either isomorphic or Morita equivalent rings. We also show that anti-isomorphisms between endomorphism rings of infinitely generated projective modules may exist

Pistas fósiles y dubiofósiles del Ediacárico y Cámbrico del Anticlinal de Alcudia, España

The fossil record of the Ediacaran—Cambrian transition in Spain provides potentially useful information to understand this critical episode in the history of life on Earth. In the present work, new findings of trace fossils and dubiofossils are described from the upper Ediacaran and lowermost Cambrian of the Alcudian unit in the Alcudia Anticline, at the southern margin of the Central Iberian Zone (valle de Alcudia, Iberian Massif, Spain). Two new trace fossil sites are described from the Upper Alcudian subunit and assigned to the Fortunian stage (lower Cambrian, Terreneuvian series) and to the regional Lower Corduban substage. They contain examples of arthropod-like scratches (Monomorphichnus lineatus), small bilobed trails (similar to Archaeonassa), an inclined burrow with spreite (may be a teichichnid), and long unbranched burrows with very fine transversal structure (probably the ventral surface of Psammichnites). Torrowangea aff. rosei and possible body fossils of late Ediacaran age are described from the Lower Alcudian subunit, including a disc resembling a frond holdfast and a diamond-shaped complex structure with no known equivalents.El registro fósil de la transición Ediacárico—Cámbrico en España proporciona información potencialmente útil para entender este episodio crítico de la historia de la vida en La Tierra. El presente trabajo describe nuevos hallazgos de icnofósiles y dubiofósiles del Ediacárico superior y Cámbrico basal en la unidad Alcudiense del Anticlinal de Alcudia, hacia el margen meridional de la Zona Centroibérica (valle de Alcudia, Macizo Ibérico, España). Dos localidades con pistas fósiles son descritas para la subunidad Alcudiense Superior, y asignadas al piso Fortuniense (Cámbrico inferior, serie Terreneuviense) y al subpiso regional Cordubiense Inferior. Contienen ejemplos de marcas de artrópodos u organismos similares (Monomorphichnus lineatus) y pistas bilobadas simples (semejantes a Archaeonassa), una madriguera con spreite inclinada (quizá un teichíchnido) y madrigueras largas, sin ramificar, con estructura transversal muy fina (probablemente la superficie ventral de Psammichnites). Se describen Torrowangea aff. rosei y posibles fósiles corporales de edad ediacárica tardía en la subunidad Alcudiense Inferior, incluyendo un disco semejante al anclaje de un fronde, y una estructura compleja, con forma de diamante, sin equivalentes conocidos

Una biota transicional Ediacárica–Cámbrica en el anticlinal de Abenójar (Macizo Ibérico, España)

A sequence with a transitional Ediacaran–Cambrian biota is described from the Navezuelas stream valley, in the Abenójar anticline (Ibor Group, Central Iberian Zone, Spain). The sequence starts with fine-grained siliciclastics containing Vendotaenia antiqua and moulds of the early skeletal fossil Cloudina cf. hartmannae. These beds are followed by carbonates with Cloudina co-occurring at hand sample level with Vendotaenia antiqua together with protoconodonts similar to Protohertzina unguliformis, suggesting a terminal Ediacaran or lowermost Cambrian age. The detrital beds above this level have simple trace fossils of deposit feeders. Above an upper carbonate bed with tiny vendotaenids there is a trace fossil assemblage of Cambrian aspect, including Treptichnus pedum and ornamented burrows resembling the ventral surface of Psammichnites. The occurrence of protoconodonts is new to the Ediacaran–Cambrian transition in Europe, and this is the third time worldwide that these typically Cambrian fossils are found co-occurring unambiguously with the typically Ediacaran cloudinids, which suggests that the Ediacaran–Cambrian transition was biologically more gradual than previously thought.Se describe una secuencia conteniendo una biota transicional ediacárica–cámbrica, en el valle del arroyo de las Navezuelas, anticlinal de Abenójar (Grupo Ibor, Zona Centroibérica, España). La secuencia empieza con capas siliciclásticas de grano fino conteniendo Vendotaenia antiqua y moldes de Cloudina cf. hartmannae, uno de los primeros animales con esqueleto mineralizado. Continúa con carbonatos con Cloudina fosfatizadas, coincidiendo en muestra de mano con Vendotaenia antiqua y con protoconodontos semejantes a Protohertzina unguliformis, lo cual sugiere una edad ediacárica terminal o cámbrica basal. Las capas detríticas sobre este nivel contienen pistas fósiles simples de organismos sedimentívoros. Sobre un estrato superior de carbonatos con pequeños vendoténidos se ha hallado un conjunto de pistas fósiles de aspecto cámbrico, incluyendo Treptichnus pedum y madrigueras ornamentadas semejantes a la superficie ventral de Psammichnites. El hallazgo de protoconodontos es nuevo para la transición Ediacárico–Cámbrico en Europa, y esta es la tercera vez a escala mundial que este tipo de fósiles típicamente cámbricos son hallados junto con cloudínidos, típicamente ediacáricos, lo cual sugiere que la transición Ediacárico–Cámbrico fue biológicamente más gradual de lo que se pensaba anteriormente

Modeling Network Populations via Graph Distances

This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fr\'{e}chet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience.Comment: 33 pages, 8 figure

The Cocoon Nebula and its ionizing star: do stellar and nebular abundances agree?

(Abridged) Main sequence massive stars embedded in an HII region should have the same chemical abundances as the surrounding nebular gas+dust. The Cocoon nebula, a close-by Galactic HII region ionized by a narrow line B0.5 V single star (BD+46 3474), is an ideal target to perform a detailed comparison of nebular and stellar abundances in the same Galactic HII region. We investigate the chemical content of O, N and S in the Cocoon nebula from two different points of view: an empirical analysis of the nebular spectrum and a detailed spectroscopic analysis of its ionizing B-type star using state-of-the-art stellar atmosphere modeling. By comparing the stellar and nebular abundances, we aim to indirectly address the long-standing problem of the discrepancy found between abundances obtained from collisionally excited lines (CELs) and optical recombination lines in photoionized nebulae. We collect spatially resolved spectroscopy of the Cocoon nebula and a high resolution optical spectrum of its ionizing star. Standard nebular techniques are used to compute the physical conditions and gaseous abundances of O, N and S. We perform a self-consistent spectroscopic abundance analysis of BD+46 3474 based on the atmosphere code FASTWIND to determine the stellar parameters and Si, O, and N abundances. The Cocoon nebula and its ionizing star, located at a distance of 800+-80 pc, have a very similar chemical composition as the Orion nebula and other B-type stars in the solar vicinity. This result agrees with the high degree of homogeneity of the present-day composition of the solar neighbourhood as derived from the study of the local cold-gas ISM. The comparison of stellar and nebular CELs abundances in the Cocoon nebula indicates that O and N gas+dust nebular values are in better agreement with stellar ones assuming small temperature fluctuations, of the order of those found in the Orion nebula.Comment: Accepted for publication in A&A. 13 pages, 7 tables and 6 figure

Supersymmetric Kerr--anti-deSitter solutions

We prove the existence of one quarter supersymmetric type IIB configurations that arise as non-trivial scaling solutions of the standard five dimensional Kerr-AdS black holes by the explicit construction of its Killing spinors. This neutral, spinning solution is asymptotic to the static anti-deSitter space-time with cosmological constant $-\textstyle{\frac{1}{\ell^2}}$, it has two finite equal angular momenta $J_1=\pm J_2$, mass $M=\textstyle{\frac{1}{\ell}} (|J_1|+|J_2|)$ and a naked singularity.We also address the scaling limit associated with one half supersymmetric solution with only one angular momentum.Comment: 15 pages, no figure